Question

Find numerically the greatest term in the expansion of ${(2+3x)}^9$ when $x=\frac{3}{2}$

Answer 1

Hence
$r=\frac{(9+1).\frac{3}{2}}{1+\frac{3}{2}}$
$=\frac{10.3}{5}=6$
Hence the 7th term will be numerically greatest term.
Hence coefficient will be
$T_7={}^9{C}_6{.2}^3{.3}^6(x{)}^6$
$={\mathrm{84.8.3}}^6.\frac{3^6}{2^6}$
$=\frac{{7.3}^{13}}{2}$